Relative Q-Gradings from Bordered Floer Theory
نویسندگان
چکیده
منابع مشابه
A tour of bordered Floer theory
Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with extended-TQFT-type gluing properties. In this survey, we explain the formal struc...
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Heegaard Floer homology, first introduced by P. Ozsváth and Z. Szabó in [OS04b], associates to a 3-manifold Y a family of relatively graded abelian groups HF (Y, t), indexed by Spin structures t on Y . In the case that Y is a rational homology sphere, Ozsváth and Szabó lift the relative Z-grading to an absolute Q-grading [OS06]. This induces a relative Q-grading on ⊕ t∈Spin(Y ) HF (Y, t). In th...
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We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented two-manifold a di erential graded algebra. For a three-manifold with speci ed boundary, the invariant comes in two di erent versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-de ned up to chain homotopy equivale...
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We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for studying bordered invariants of this form and, in particular, provide a complete description of slopes giving rise to L-space Dehn fillings as well as neces...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2018
ISSN: 0026-2285
DOI: 10.1307/mmj/1539763499